On the Mordell-Weil rank of an abelian variety over a number field
The authors give a bound for the rank of the Mordell-Weil group of an abelian variety A over a number-field K. The bound depends only on the dimension, the degree [K:\({\mathbb{Q}}]\) and the conductor of A. The proof uses the injection \(A(K)/2\cdot A(k)\subseteq H^ 1(K,A[2])\), and a bound on the order of the cohomology obtained by estimating discriminants.
bound for the rank of the Mordell-Weil group
scientific article; zbMATH DE number 4123881
scientific article